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Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Millions
 3 Months Ended 6 Months Ended
Dec. 03, 2022
Sep. 03, 2022
Nov. 27, 2021
Aug. 28, 2021
Dec. 03, 2022
Nov. 27, 2021
Accumulated Other Comprehensive Income [Roll Forward]            
Balance at beginning of period   $ 1,427.1     $ 1,427.1  
Other comprehensive (loss) income, net of tax before reclassifications         (8.8) $ (45.2)
Reclassification from accumulated other comprehensive loss - Other, net         3.1 2.8
Tax benefit         (0.3) (0.6)
Net reclassifications         2.8 2.2
Other comprehensive income (loss), net of tax $ 51.8 (57.8) $ (27.8) $ (15.2) (6.0) (43.0)
Balance at end of period 1,434.3       1,434.3  
Accumulated Other Comprehensive Loss            
Accumulated Other Comprehensive Income [Roll Forward]            
Balance at beginning of period   (107.1)   (65.1) (107.1) (65.1)
Other comprehensive income (loss), net of tax 51.8 (57.8) (27.8) (15.2)    
Balance at end of period (113.1)   (108.1)   (113.1) (108.1)
Cumulative Translation Adjustments            
Accumulated Other Comprehensive Income [Roll Forward]            
Balance at beginning of period   (93.9)   (3.9) (93.9) (3.9)
Other comprehensive (loss) income, net of tax before reclassifications         (28.3) (50.1)
Reclassification from accumulated other comprehensive loss - Other, net         0.0 0.0
Tax benefit         0.0 0.0
Net reclassifications         0.0 0.0
Other comprehensive income (loss), net of tax         (28.3) (50.1)
Balance at end of period (122.2)   (54.0)   (122.2) (54.0)
Pension and Other Post-retirement Benefit Plans            
Accumulated Other Comprehensive Income [Roll Forward]            
Balance at beginning of period   (36.9)   (50.4) (36.9) (50.4)
Other comprehensive (loss) income, net of tax before reclassifications         0.0 0.0
Reclassification from accumulated other comprehensive loss - Other, net         1.1 4.7
Tax benefit         (0.3) (0.6)
Net reclassifications         0.8 4.1
Other comprehensive income (loss), net of tax         0.8 4.1
Balance at end of period (36.1)   (46.3)   (36.1) (46.3)
Interest Rate Swap Agreement            
Accumulated Other Comprehensive Income [Roll Forward]            
Balance at beginning of period   $ 23.7   $ (10.8) 23.7 (10.8)
Other comprehensive (loss) income, net of tax before reclassifications         19.5 4.9
Reclassification from accumulated other comprehensive loss - Other, net         2.0 (1.9)
Tax benefit         0.0 0.0
Net reclassifications         2.0 (1.9)
Other comprehensive income (loss), net of tax         21.5 3.0
Balance at end of period $ 45.2   $ (7.8)   $ 45.2 $ (7.8)